http://www.youtube.com/watch?v=0Oq454v8gX0
I don't know what the song's name would be in Romaji or in English, but it's an arrange of "The Maid and the Pocket Watch of Blood" and "Luna Clock~Luna Dial," from Touhou: Embodiement of Scarlet Devil. It starts up more heavily around 47 seconds.
http://www.youtube.com/watch?v=vIDabexD5AU
Romanized, the title is "Katakoi no Tsuki." It's an arrange of "Broken Moon," a pre-battle theme from Touhou 7.5: Immaterial and Missing Power.
For the next song, have youtube annotations set to on, as there is a translation, along with song/cirle info, like who the singer is.
This is "Gensou no Sateraito," or, rather, "Fantasy Satellite." It's an arrange of "Greenwich in the Sky,' from ZUN's CD "Magical Astronomy." It really picks up at 41 seconds.
http://www.youtube.com/watch?v=8_R4Em7lkkQ
http://www.youtube.com/watch?v=0ramXzlCtfo
Hey, "Bad Apple!" is a good song. The annotations will name all of the characters for you if you don't know them.
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Keep the annotations on again, as the English Translation is done through them.
This is anarrange of "Beware the Umbrella Left There Forever,' from Touhou 12: Undefined Fantastic Object (UFO). Nice PV, righ?
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This is an arrange of "Bell of Avici ~ Infinite Nightmare," from Touhou 12.5: Double Spoiler.
The PV was done by the same person as the above one, even if the arrange was by someone else.